Viewing File: /home/ubuntu/combine_ai/combine/lib/python3.10/site-packages/sympy/core/assumptions_generated.py
"""
Do NOT manually edit this file.
Instead, run ./bin/ask_update.py.
"""
defined_facts = [
'algebraic',
'antihermitian',
'commutative',
'complex',
'composite',
'even',
'extended_negative',
'extended_nonnegative',
'extended_nonpositive',
'extended_nonzero',
'extended_positive',
'extended_real',
'finite',
'hermitian',
'imaginary',
'infinite',
'integer',
'irrational',
'negative',
'noninteger',
'nonnegative',
'nonpositive',
'nonzero',
'odd',
'positive',
'prime',
'rational',
'real',
'transcendental',
'zero',
] # defined_facts
full_implications = dict( [
# Implications of algebraic = True:
(('algebraic', True), set( (
('commutative', True),
('complex', True),
('finite', True),
('infinite', False),
('transcendental', False),
) ),
),
# Implications of algebraic = False:
(('algebraic', False), set( (
('composite', False),
('even', False),
('integer', False),
('odd', False),
('prime', False),
('rational', False),
('zero', False),
) ),
),
# Implications of antihermitian = True:
(('antihermitian', True), set( (
) ),
),
# Implications of antihermitian = False:
(('antihermitian', False), set( (
('imaginary', False),
) ),
),
# Implications of commutative = True:
(('commutative', True), set( (
) ),
),
# Implications of commutative = False:
(('commutative', False), set( (
('algebraic', False),
('complex', False),
('composite', False),
('even', False),
('extended_negative', False),
('extended_nonnegative', False),
('extended_nonpositive', False),
('extended_nonzero', False),
('extended_positive', False),
('extended_real', False),
('imaginary', False),
('integer', False),
('irrational', False),
('negative', False),
('noninteger', False),
('nonnegative', False),
('nonpositive', False),
('nonzero', False),
('odd', False),
('positive', False),
('prime', False),
('rational', False),
('real', False),
('transcendental', False),
('zero', False),
) ),
),
# Implications of complex = True:
(('complex', True), set( (
('commutative', True),
('finite', True),
('infinite', False),
) ),
),
# Implications of complex = False:
(('complex', False), set( (
('algebraic', False),
('composite', False),
('even', False),
('imaginary', False),
('integer', False),
('irrational', False),
('negative', False),
('nonnegative', False),
('nonpositive', False),
('nonzero', False),
('odd', False),
('positive', False),
('prime', False),
('rational', False),
('real', False),
('transcendental', False),
('zero', False),
) ),
),
# Implications of composite = True:
(('composite', True), set( (
('algebraic', True),
('commutative', True),
('complex', True),
('extended_negative', False),
('extended_nonnegative', True),
('extended_nonpositive', False),
('extended_nonzero', True),
('extended_positive', True),
('extended_real', True),
('finite', True),
('hermitian', True),
('imaginary', False),
('infinite', False),
('integer', True),
('irrational', False),
('negative', False),
('noninteger', False),
('nonnegative', True),
('nonpositive', False),
('nonzero', True),
('positive', True),
('prime', False),
('rational', True),
('real', True),
('transcendental', False),
('zero', False),
) ),
),
# Implications of composite = False:
(('composite', False), set( (
) ),
),
# Implications of even = True:
(('even', True), set( (
('algebraic', True),
('commutative', True),
('complex', True),
('extended_real', True),
('finite', True),
('hermitian', True),
('imaginary', False),
('infinite', False),
('integer', True),
('irrational', False),
('noninteger', False),
('odd', False),
('rational', True),
('real', True),
('transcendental', False),
) ),
),
# Implications of even = False:
(('even', False), set( (
('zero', False),
) ),
),
# Implications of extended_negative = True:
(('extended_negative', True), set( (
('commutative', True),
('composite', False),
('extended_nonnegative', False),
('extended_nonpositive', True),
('extended_nonzero', True),
('extended_positive', False),
('extended_real', True),
('imaginary', False),
('nonnegative', False),
('positive', False),
('prime', False),
('zero', False),
) ),
),
# Implications of extended_negative = False:
(('extended_negative', False), set( (
('negative', False),
) ),
),
# Implications of extended_nonnegative = True:
(('extended_nonnegative', True), set( (
('commutative', True),
('extended_negative', False),
('extended_real', True),
('imaginary', False),
('negative', False),
) ),
),
# Implications of extended_nonnegative = False:
(('extended_nonnegative', False), set( (
('composite', False),
('extended_positive', False),
('nonnegative', False),
('positive', False),
('prime', False),
('zero', False),
) ),
),
# Implications of extended_nonpositive = True:
(('extended_nonpositive', True), set( (
('commutative', True),
('composite', False),
('extended_positive', False),
('extended_real', True),
('imaginary', False),
('positive', False),
('prime', False),
) ),
),
# Implications of extended_nonpositive = False:
(('extended_nonpositive', False), set( (
('extended_negative', False),
('negative', False),
('nonpositive', False),
('zero', False),
) ),
),
# Implications of extended_nonzero = True:
(('extended_nonzero', True), set( (
('commutative', True),
('extended_real', True),
('imaginary', False),
('zero', False),
) ),
),
# Implications of extended_nonzero = False:
(('extended_nonzero', False), set( (
('composite', False),
('extended_negative', False),
('extended_positive', False),
('negative', False),
('nonzero', False),
('positive', False),
('prime', False),
) ),
),
# Implications of extended_positive = True:
(('extended_positive', True), set( (
('commutative', True),
('extended_negative', False),
('extended_nonnegative', True),
('extended_nonpositive', False),
('extended_nonzero', True),
('extended_real', True),
('imaginary', False),
('negative', False),
('nonpositive', False),
('zero', False),
) ),
),
# Implications of extended_positive = False:
(('extended_positive', False), set( (
('composite', False),
('positive', False),
('prime', False),
) ),
),
# Implications of extended_real = True:
(('extended_real', True), set( (
('commutative', True),
('imaginary', False),
) ),
),
# Implications of extended_real = False:
(('extended_real', False), set( (
('composite', False),
('even', False),
('extended_negative', False),
('extended_nonnegative', False),
('extended_nonpositive', False),
('extended_nonzero', False),
('extended_positive', False),
('integer', False),
('irrational', False),
('negative', False),
('noninteger', False),
('nonnegative', False),
('nonpositive', False),
('nonzero', False),
('odd', False),
('positive', False),
('prime', False),
('rational', False),
('real', False),
('zero', False),
) ),
),
# Implications of finite = True:
(('finite', True), set( (
('infinite', False),
) ),
),
# Implications of finite = False:
(('finite', False), set( (
('algebraic', False),
('complex', False),
('composite', False),
('even', False),
('imaginary', False),
('infinite', True),
('integer', False),
('irrational', False),
('negative', False),
('nonnegative', False),
('nonpositive', False),
('nonzero', False),
('odd', False),
('positive', False),
('prime', False),
('rational', False),
('real', False),
('transcendental', False),
('zero', False),
) ),
),
# Implications of hermitian = True:
(('hermitian', True), set( (
) ),
),
# Implications of hermitian = False:
(('hermitian', False), set( (
('composite', False),
('even', False),
('integer', False),
('irrational', False),
('negative', False),
('nonnegative', False),
('nonpositive', False),
('nonzero', False),
('odd', False),
('positive', False),
('prime', False),
('rational', False),
('real', False),
('zero', False),
) ),
),
# Implications of imaginary = True:
(('imaginary', True), set( (
('antihermitian', True),
('commutative', True),
('complex', True),
('composite', False),
('even', False),
('extended_negative', False),
('extended_nonnegative', False),
('extended_nonpositive', False),
('extended_nonzero', False),
('extended_positive', False),
('extended_real', False),
('finite', True),
('infinite', False),
('integer', False),
('irrational', False),
('negative', False),
('noninteger', False),
('nonnegative', False),
('nonpositive', False),
('nonzero', False),
('odd', False),
('positive', False),
('prime', False),
('rational', False),
('real', False),
('zero', False),
) ),
),
# Implications of imaginary = False:
(('imaginary', False), set( (
) ),
),
# Implications of infinite = True:
(('infinite', True), set( (
('algebraic', False),
('complex', False),
('composite', False),
('even', False),
('finite', False),
('imaginary', False),
('integer', False),
('irrational', False),
('negative', False),
('nonnegative', False),
('nonpositive', False),
('nonzero', False),
('odd', False),
('positive', False),
('prime', False),
('rational', False),
('real', False),
('transcendental', False),
('zero', False),
) ),
),
# Implications of infinite = False:
(('infinite', False), set( (
('finite', True),
) ),
),
# Implications of integer = True:
(('integer', True), set( (
('algebraic', True),
('commutative', True),
('complex', True),
('extended_real', True),
('finite', True),
('hermitian', True),
('imaginary', False),
('infinite', False),
('irrational', False),
('noninteger', False),
('rational', True),
('real', True),
('transcendental', False),
) ),
),
# Implications of integer = False:
(('integer', False), set( (
('composite', False),
('even', False),
('odd', False),
('prime', False),
('zero', False),
) ),
),
# Implications of irrational = True:
(('irrational', True), set( (
('commutative', True),
('complex', True),
('composite', False),
('even', False),
('extended_nonzero', True),
('extended_real', True),
('finite', True),
('hermitian', True),
('imaginary', False),
('infinite', False),
('integer', False),
('noninteger', True),
('nonzero', True),
('odd', False),
('prime', False),
('rational', False),
('real', True),
('zero', False),
) ),
),
# Implications of irrational = False:
(('irrational', False), set( (
) ),
),
# Implications of negative = True:
(('negative', True), set( (
('commutative', True),
('complex', True),
('composite', False),
('extended_negative', True),
('extended_nonnegative', False),
('extended_nonpositive', True),
('extended_nonzero', True),
('extended_positive', False),
('extended_real', True),
('finite', True),
('hermitian', True),
('imaginary', False),
('infinite', False),
('nonnegative', False),
('nonpositive', True),
('nonzero', True),
('positive', False),
('prime', False),
('real', True),
('zero', False),
) ),
),
# Implications of negative = False:
(('negative', False), set( (
) ),
),
# Implications of noninteger = True:
(('noninteger', True), set( (
('commutative', True),
('composite', False),
('even', False),
('extended_nonzero', True),
('extended_real', True),
('imaginary', False),
('integer', False),
('odd', False),
('prime', False),
('zero', False),
) ),
),
# Implications of noninteger = False:
(('noninteger', False), set( (
) ),
),
# Implications of nonnegative = True:
(('nonnegative', True), set( (
('commutative', True),
('complex', True),
('extended_negative', False),
('extended_nonnegative', True),
('extended_real', True),
('finite', True),
('hermitian', True),
('imaginary', False),
('infinite', False),
('negative', False),
('real', True),
) ),
),
# Implications of nonnegative = False:
(('nonnegative', False), set( (
('composite', False),
('positive', False),
('prime', False),
('zero', False),
) ),
),
# Implications of nonpositive = True:
(('nonpositive', True), set( (
('commutative', True),
('complex', True),
('composite', False),
('extended_nonpositive', True),
('extended_positive', False),
('extended_real', True),
('finite', True),
('hermitian', True),
('imaginary', False),
('infinite', False),
('positive', False),
('prime', False),
('real', True),
) ),
),
# Implications of nonpositive = False:
(('nonpositive', False), set( (
('negative', False),
('zero', False),
) ),
),
# Implications of nonzero = True:
(('nonzero', True), set( (
('commutative', True),
('complex', True),
('extended_nonzero', True),
('extended_real', True),
('finite', True),
('hermitian', True),
('imaginary', False),
('infinite', False),
('real', True),
('zero', False),
) ),
),
# Implications of nonzero = False:
(('nonzero', False), set( (
('composite', False),
('negative', False),
('positive', False),
('prime', False),
) ),
),
# Implications of odd = True:
(('odd', True), set( (
('algebraic', True),
('commutative', True),
('complex', True),
('even', False),
('extended_nonzero', True),
('extended_real', True),
('finite', True),
('hermitian', True),
('imaginary', False),
('infinite', False),
('integer', True),
('irrational', False),
('noninteger', False),
('nonzero', True),
('rational', True),
('real', True),
('transcendental', False),
('zero', False),
) ),
),
# Implications of odd = False:
(('odd', False), set( (
) ),
),
# Implications of positive = True:
(('positive', True), set( (
('commutative', True),
('complex', True),
('extended_negative', False),
('extended_nonnegative', True),
('extended_nonpositive', False),
('extended_nonzero', True),
('extended_positive', True),
('extended_real', True),
('finite', True),
('hermitian', True),
('imaginary', False),
('infinite', False),
('negative', False),
('nonnegative', True),
('nonpositive', False),
('nonzero', True),
('real', True),
('zero', False),
) ),
),
# Implications of positive = False:
(('positive', False), set( (
('composite', False),
('prime', False),
) ),
),
# Implications of prime = True:
(('prime', True), set( (
('algebraic', True),
('commutative', True),
('complex', True),
('composite', False),
('extended_negative', False),
('extended_nonnegative', True),
('extended_nonpositive', False),
('extended_nonzero', True),
('extended_positive', True),
('extended_real', True),
('finite', True),
('hermitian', True),
('imaginary', False),
('infinite', False),
('integer', True),
('irrational', False),
('negative', False),
('noninteger', False),
('nonnegative', True),
('nonpositive', False),
('nonzero', True),
('positive', True),
('rational', True),
('real', True),
('transcendental', False),
('zero', False),
) ),
),
# Implications of prime = False:
(('prime', False), set( (
) ),
),
# Implications of rational = True:
(('rational', True), set( (
('algebraic', True),
('commutative', True),
('complex', True),
('extended_real', True),
('finite', True),
('hermitian', True),
('imaginary', False),
('infinite', False),
('irrational', False),
('real', True),
('transcendental', False),
) ),
),
# Implications of rational = False:
(('rational', False), set( (
('composite', False),
('even', False),
('integer', False),
('odd', False),
('prime', False),
('zero', False),
) ),
),
# Implications of real = True:
(('real', True), set( (
('commutative', True),
('complex', True),
('extended_real', True),
('finite', True),
('hermitian', True),
('imaginary', False),
('infinite', False),
) ),
),
# Implications of real = False:
(('real', False), set( (
('composite', False),
('even', False),
('integer', False),
('irrational', False),
('negative', False),
('nonnegative', False),
('nonpositive', False),
('nonzero', False),
('odd', False),
('positive', False),
('prime', False),
('rational', False),
('zero', False),
) ),
),
# Implications of transcendental = True:
(('transcendental', True), set( (
('algebraic', False),
('commutative', True),
('complex', True),
('composite', False),
('even', False),
('finite', True),
('infinite', False),
('integer', False),
('odd', False),
('prime', False),
('rational', False),
('zero', False),
) ),
),
# Implications of transcendental = False:
(('transcendental', False), set( (
) ),
),
# Implications of zero = True:
(('zero', True), set( (
('algebraic', True),
('commutative', True),
('complex', True),
('composite', False),
('even', True),
('extended_negative', False),
('extended_nonnegative', True),
('extended_nonpositive', True),
('extended_nonzero', False),
('extended_positive', False),
('extended_real', True),
('finite', True),
('hermitian', True),
('imaginary', False),
('infinite', False),
('integer', True),
('irrational', False),
('negative', False),
('noninteger', False),
('nonnegative', True),
('nonpositive', True),
('nonzero', False),
('odd', False),
('positive', False),
('prime', False),
('rational', True),
('real', True),
('transcendental', False),
) ),
),
# Implications of zero = False:
(('zero', False), set( (
) ),
),
] ) # full_implications
prereq = {
# facts that could determine the value of algebraic
'algebraic': {
'commutative',
'complex',
'composite',
'even',
'finite',
'infinite',
'integer',
'odd',
'prime',
'rational',
'transcendental',
'zero',
},
# facts that could determine the value of antihermitian
'antihermitian': {
'imaginary',
},
# facts that could determine the value of commutative
'commutative': {
'algebraic',
'complex',
'composite',
'even',
'extended_negative',
'extended_nonnegative',
'extended_nonpositive',
'extended_nonzero',
'extended_positive',
'extended_real',
'imaginary',
'integer',
'irrational',
'negative',
'noninteger',
'nonnegative',
'nonpositive',
'nonzero',
'odd',
'positive',
'prime',
'rational',
'real',
'transcendental',
'zero',
},
# facts that could determine the value of complex
'complex': {
'algebraic',
'commutative',
'composite',
'even',
'finite',
'imaginary',
'infinite',
'integer',
'irrational',
'negative',
'nonnegative',
'nonpositive',
'nonzero',
'odd',
'positive',
'prime',
'rational',
'real',
'transcendental',
'zero',
},
# facts that could determine the value of composite
'composite': {
'algebraic',
'commutative',
'complex',
'extended_negative',
'extended_nonnegative',
'extended_nonpositive',
'extended_nonzero',
'extended_positive',
'extended_real',
'finite',
'hermitian',
'imaginary',
'infinite',
'integer',
'irrational',
'negative',
'noninteger',
'nonnegative',
'nonpositive',
'nonzero',
'positive',
'prime',
'rational',
'real',
'transcendental',
'zero',
},
# facts that could determine the value of even
'even': {
'algebraic',
'commutative',
'complex',
'extended_real',
'finite',
'hermitian',
'imaginary',
'infinite',
'integer',
'irrational',
'noninteger',
'odd',
'rational',
'real',
'transcendental',
'zero',
},
# facts that could determine the value of extended_negative
'extended_negative': {
'commutative',
'composite',
'extended_nonnegative',
'extended_nonpositive',
'extended_nonzero',
'extended_positive',
'extended_real',
'imaginary',
'negative',
'nonnegative',
'positive',
'prime',
'zero',
},
# facts that could determine the value of extended_nonnegative
'extended_nonnegative': {
'commutative',
'composite',
'extended_negative',
'extended_positive',
'extended_real',
'imaginary',
'negative',
'nonnegative',
'positive',
'prime',
'zero',
},
# facts that could determine the value of extended_nonpositive
'extended_nonpositive': {
'commutative',
'composite',
'extended_negative',
'extended_positive',
'extended_real',
'imaginary',
'negative',
'nonpositive',
'positive',
'prime',
'zero',
},
# facts that could determine the value of extended_nonzero
'extended_nonzero': {
'commutative',
'composite',
'extended_negative',
'extended_positive',
'extended_real',
'imaginary',
'irrational',
'negative',
'noninteger',
'nonzero',
'odd',
'positive',
'prime',
'zero',
},
# facts that could determine the value of extended_positive
'extended_positive': {
'commutative',
'composite',
'extended_negative',
'extended_nonnegative',
'extended_nonpositive',
'extended_nonzero',
'extended_real',
'imaginary',
'negative',
'nonpositive',
'positive',
'prime',
'zero',
},
# facts that could determine the value of extended_real
'extended_real': {
'commutative',
'composite',
'even',
'extended_negative',
'extended_nonnegative',
'extended_nonpositive',
'extended_nonzero',
'extended_positive',
'imaginary',
'integer',
'irrational',
'negative',
'noninteger',
'nonnegative',
'nonpositive',
'nonzero',
'odd',
'positive',
'prime',
'rational',
'real',
'zero',
},
# facts that could determine the value of finite
'finite': {
'algebraic',
'complex',
'composite',
'even',
'imaginary',
'infinite',
'integer',
'irrational',
'negative',
'nonnegative',
'nonpositive',
'nonzero',
'odd',
'positive',
'prime',
'rational',
'real',
'transcendental',
'zero',
},
# facts that could determine the value of hermitian
'hermitian': {
'composite',
'even',
'integer',
'irrational',
'negative',
'nonnegative',
'nonpositive',
'nonzero',
'odd',
'positive',
'prime',
'rational',
'real',
'zero',
},
# facts that could determine the value of imaginary
'imaginary': {
'antihermitian',
'commutative',
'complex',
'composite',
'even',
'extended_negative',
'extended_nonnegative',
'extended_nonpositive',
'extended_nonzero',
'extended_positive',
'extended_real',
'finite',
'infinite',
'integer',
'irrational',
'negative',
'noninteger',
'nonnegative',
'nonpositive',
'nonzero',
'odd',
'positive',
'prime',
'rational',
'real',
'zero',
},
# facts that could determine the value of infinite
'infinite': {
'algebraic',
'complex',
'composite',
'even',
'finite',
'imaginary',
'integer',
'irrational',
'negative',
'nonnegative',
'nonpositive',
'nonzero',
'odd',
'positive',
'prime',
'rational',
'real',
'transcendental',
'zero',
},
# facts that could determine the value of integer
'integer': {
'algebraic',
'commutative',
'complex',
'composite',
'even',
'extended_real',
'finite',
'hermitian',
'imaginary',
'infinite',
'irrational',
'noninteger',
'odd',
'prime',
'rational',
'real',
'transcendental',
'zero',
},
# facts that could determine the value of irrational
'irrational': {
'commutative',
'complex',
'composite',
'even',
'extended_real',
'finite',
'hermitian',
'imaginary',
'infinite',
'integer',
'odd',
'prime',
'rational',
'real',
'zero',
},
# facts that could determine the value of negative
'negative': {
'commutative',
'complex',
'composite',
'extended_negative',
'extended_nonnegative',
'extended_nonpositive',
'extended_nonzero',
'extended_positive',
'extended_real',
'finite',
'hermitian',
'imaginary',
'infinite',
'nonnegative',
'nonpositive',
'nonzero',
'positive',
'prime',
'real',
'zero',
},
# facts that could determine the value of noninteger
'noninteger': {
'commutative',
'composite',
'even',
'extended_real',
'imaginary',
'integer',
'irrational',
'odd',
'prime',
'zero',
},
# facts that could determine the value of nonnegative
'nonnegative': {
'commutative',
'complex',
'composite',
'extended_negative',
'extended_nonnegative',
'extended_real',
'finite',
'hermitian',
'imaginary',
'infinite',
'negative',
'positive',
'prime',
'real',
'zero',
},
# facts that could determine the value of nonpositive
'nonpositive': {
'commutative',
'complex',
'composite',
'extended_nonpositive',
'extended_positive',
'extended_real',
'finite',
'hermitian',
'imaginary',
'infinite',
'negative',
'positive',
'prime',
'real',
'zero',
},
# facts that could determine the value of nonzero
'nonzero': {
'commutative',
'complex',
'composite',
'extended_nonzero',
'extended_real',
'finite',
'hermitian',
'imaginary',
'infinite',
'irrational',
'negative',
'odd',
'positive',
'prime',
'real',
'zero',
},
# facts that could determine the value of odd
'odd': {
'algebraic',
'commutative',
'complex',
'even',
'extended_real',
'finite',
'hermitian',
'imaginary',
'infinite',
'integer',
'irrational',
'noninteger',
'rational',
'real',
'transcendental',
'zero',
},
# facts that could determine the value of positive
'positive': {
'commutative',
'complex',
'composite',
'extended_negative',
'extended_nonnegative',
'extended_nonpositive',
'extended_nonzero',
'extended_positive',
'extended_real',
'finite',
'hermitian',
'imaginary',
'infinite',
'negative',
'nonnegative',
'nonpositive',
'nonzero',
'prime',
'real',
'zero',
},
# facts that could determine the value of prime
'prime': {
'algebraic',
'commutative',
'complex',
'composite',
'extended_negative',
'extended_nonnegative',
'extended_nonpositive',
'extended_nonzero',
'extended_positive',
'extended_real',
'finite',
'hermitian',
'imaginary',
'infinite',
'integer',
'irrational',
'negative',
'noninteger',
'nonnegative',
'nonpositive',
'nonzero',
'positive',
'rational',
'real',
'transcendental',
'zero',
},
# facts that could determine the value of rational
'rational': {
'algebraic',
'commutative',
'complex',
'composite',
'even',
'extended_real',
'finite',
'hermitian',
'imaginary',
'infinite',
'integer',
'irrational',
'odd',
'prime',
'real',
'transcendental',
'zero',
},
# facts that could determine the value of real
'real': {
'commutative',
'complex',
'composite',
'even',
'extended_real',
'finite',
'hermitian',
'imaginary',
'infinite',
'integer',
'irrational',
'negative',
'nonnegative',
'nonpositive',
'nonzero',
'odd',
'positive',
'prime',
'rational',
'zero',
},
# facts that could determine the value of transcendental
'transcendental': {
'algebraic',
'commutative',
'complex',
'composite',
'even',
'finite',
'infinite',
'integer',
'odd',
'prime',
'rational',
'zero',
},
# facts that could determine the value of zero
'zero': {
'algebraic',
'commutative',
'complex',
'composite',
'even',
'extended_negative',
'extended_nonnegative',
'extended_nonpositive',
'extended_nonzero',
'extended_positive',
'extended_real',
'finite',
'hermitian',
'imaginary',
'infinite',
'integer',
'irrational',
'negative',
'noninteger',
'nonnegative',
'nonpositive',
'nonzero',
'odd',
'positive',
'prime',
'rational',
'real',
'transcendental',
},
} # prereq
# Note: the order of the beta rules is used in the beta_triggers
beta_rules = [
# Rules implying composite = True
({('even', True), ('positive', True), ('prime', False)},
('composite', True)),
# Rules implying even = False
({('composite', False), ('positive', True), ('prime', False)},
('even', False)),
# Rules implying even = True
({('integer', True), ('odd', False)},
('even', True)),
# Rules implying extended_negative = True
({('extended_positive', False), ('extended_real', True), ('zero', False)},
('extended_negative', True)),
({('extended_nonpositive', True), ('extended_nonzero', True)},
('extended_negative', True)),
# Rules implying extended_nonnegative = True
({('extended_negative', False), ('extended_real', True)},
('extended_nonnegative', True)),
# Rules implying extended_nonpositive = True
({('extended_positive', False), ('extended_real', True)},
('extended_nonpositive', True)),
# Rules implying extended_nonzero = True
({('extended_real', True), ('zero', False)},
('extended_nonzero', True)),
# Rules implying extended_positive = True
({('extended_negative', False), ('extended_real', True), ('zero', False)},
('extended_positive', True)),
({('extended_nonnegative', True), ('extended_nonzero', True)},
('extended_positive', True)),
# Rules implying extended_real = False
({('infinite', False), ('real', False)},
('extended_real', False)),
({('extended_negative', False), ('extended_positive', False), ('zero', False)},
('extended_real', False)),
# Rules implying infinite = True
({('extended_real', True), ('real', False)},
('infinite', True)),
# Rules implying irrational = True
({('rational', False), ('real', True)},
('irrational', True)),
# Rules implying negative = True
({('positive', False), ('real', True), ('zero', False)},
('negative', True)),
({('nonpositive', True), ('nonzero', True)},
('negative', True)),
({('extended_negative', True), ('finite', True)},
('negative', True)),
# Rules implying noninteger = True
({('extended_real', True), ('integer', False)},
('noninteger', True)),
# Rules implying nonnegative = True
({('negative', False), ('real', True)},
('nonnegative', True)),
({('extended_nonnegative', True), ('finite', True)},
('nonnegative', True)),
# Rules implying nonpositive = True
({('positive', False), ('real', True)},
('nonpositive', True)),
({('extended_nonpositive', True), ('finite', True)},
('nonpositive', True)),
# Rules implying nonzero = True
({('extended_nonzero', True), ('finite', True)},
('nonzero', True)),
# Rules implying odd = True
({('even', False), ('integer', True)},
('odd', True)),
# Rules implying positive = False
({('composite', False), ('even', True), ('prime', False)},
('positive', False)),
# Rules implying positive = True
({('negative', False), ('real', True), ('zero', False)},
('positive', True)),
({('nonnegative', True), ('nonzero', True)},
('positive', True)),
({('extended_positive', True), ('finite', True)},
('positive', True)),
# Rules implying prime = True
({('composite', False), ('even', True), ('positive', True)},
('prime', True)),
# Rules implying real = False
({('negative', False), ('positive', False), ('zero', False)},
('real', False)),
# Rules implying real = True
({('extended_real', True), ('infinite', False)},
('real', True)),
({('extended_real', True), ('finite', True)},
('real', True)),
# Rules implying transcendental = True
({('algebraic', False), ('complex', True)},
('transcendental', True)),
# Rules implying zero = True
({('extended_negative', False), ('extended_positive', False), ('extended_real', True)},
('zero', True)),
({('negative', False), ('positive', False), ('real', True)},
('zero', True)),
({('extended_nonnegative', True), ('extended_nonpositive', True)},
('zero', True)),
({('nonnegative', True), ('nonpositive', True)},
('zero', True)),
] # beta_rules
beta_triggers = {
('algebraic', False): [32, 11, 3, 8, 29, 14, 25, 13, 17, 7],
('algebraic', True): [10, 30, 31, 27, 16, 21, 19, 22],
('antihermitian', False): [],
('commutative', False): [],
('complex', False): [10, 12, 11, 3, 8, 17, 7],
('complex', True): [32, 10, 30, 31, 27, 16, 21, 19, 22],
('composite', False): [1, 28, 24],
('composite', True): [23, 2],
('even', False): [23, 11, 3, 8, 29, 14, 25, 7],
('even', True): [3, 33, 8, 6, 5, 14, 34, 25, 20, 18, 27, 16, 21, 19, 22, 0, 28, 24, 7],
('extended_negative', False): [11, 33, 8, 5, 29, 34, 25, 18],
('extended_negative', True): [30, 12, 31, 29, 14, 20, 16, 21, 22, 17],
('extended_nonnegative', False): [11, 3, 6, 29, 14, 20, 7],
('extended_nonnegative', True): [30, 12, 31, 33, 8, 9, 6, 29, 34, 25, 18, 19, 35, 17, 7],
('extended_nonpositive', False): [11, 8, 5, 29, 25, 18, 7],
('extended_nonpositive', True): [30, 12, 31, 3, 33, 4, 5, 29, 14, 34, 20, 21, 35, 17, 7],
('extended_nonzero', False): [11, 33, 6, 5, 29, 34, 20, 18],
('extended_nonzero', True): [30, 12, 31, 3, 8, 4, 9, 6, 5, 29, 14, 25, 22, 17],
('extended_positive', False): [11, 3, 33, 6, 29, 14, 34, 20],
('extended_positive', True): [30, 12, 31, 29, 25, 18, 27, 19, 22, 17],
('extended_real', False): [],
('extended_real', True): [30, 12, 31, 3, 33, 8, 6, 5, 17, 7],
('finite', False): [11, 3, 8, 17, 7],
('finite', True): [10, 30, 31, 27, 16, 21, 19, 22],
('hermitian', False): [10, 12, 11, 3, 8, 17, 7],
('imaginary', True): [32],
('infinite', False): [10, 30, 31, 27, 16, 21, 19, 22],
('infinite', True): [11, 3, 8, 17, 7],
('integer', False): [11, 3, 8, 29, 14, 25, 17, 7],
('integer', True): [23, 2, 3, 33, 8, 6, 5, 14, 34, 25, 20, 18, 27, 16, 21, 19, 22, 7],
('irrational', True): [32, 3, 8, 4, 9, 6, 5, 14, 25, 15, 26, 20, 18, 27, 16, 21, 19],
('negative', False): [29, 34, 25, 18],
('negative', True): [32, 13, 17],
('noninteger', True): [30, 12, 31, 3, 8, 4, 9, 6, 5, 29, 14, 25, 22],
('nonnegative', False): [11, 3, 8, 29, 14, 20, 7],
('nonnegative', True): [32, 33, 8, 9, 6, 34, 25, 26, 20, 27, 21, 22, 35, 36, 13, 17, 7],
('nonpositive', False): [11, 3, 8, 29, 25, 18, 7],
('nonpositive', True): [32, 3, 33, 4, 5, 14, 34, 15, 18, 16, 19, 22, 35, 36, 13, 17, 7],
('nonzero', False): [29, 34, 20, 18],
('nonzero', True): [32, 3, 8, 4, 9, 6, 5, 14, 25, 15, 26, 20, 18, 27, 16, 21, 19, 13, 17],
('odd', False): [2],
('odd', True): [3, 8, 4, 9, 6, 5, 14, 25, 15, 26, 20, 18, 27, 16, 21, 19],
('positive', False): [29, 14, 34, 20],
('positive', True): [32, 0, 1, 28, 13, 17],
('prime', False): [0, 1, 24],
('prime', True): [23, 2],
('rational', False): [11, 3, 8, 29, 14, 25, 13, 17, 7],
('rational', True): [3, 33, 8, 6, 5, 14, 34, 25, 20, 18, 27, 16, 21, 19, 22, 17, 7],
('real', False): [10, 12, 11, 3, 8, 17, 7],
('real', True): [32, 3, 33, 8, 6, 5, 14, 34, 25, 20, 18, 27, 16, 21, 19, 22, 13, 17, 7],
('transcendental', True): [10, 30, 31, 11, 3, 8, 29, 14, 25, 27, 16, 21, 19, 22, 13, 17, 7],
('zero', False): [11, 3, 8, 29, 14, 25, 7],
('zero', True): [],
} # beta_triggers
generated_assumptions = {'defined_facts': defined_facts, 'full_implications': full_implications,
'prereq': prereq, 'beta_rules': beta_rules, 'beta_triggers': beta_triggers}
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