Predicate Expressions and Rules

A predicate expression is a truealgebra expression that asserts a mathematical property of its subexpression(s). Often Included with predicate expressions are logical expressions such as and, or, and not.

The symbols true and false are used to represent truth and falsehood. Predicate rules evalute predicate and logic expressions to one of three results:

Symbol true: indicating that the predicate/logic expression is true. Truealgebra true is lower case to avoid confusion with python True.
Symbol false: indicating that the predicate/logic expression is false. Truealgebra false is lower case to avoid confusion with python False.
Input expressio , unevaluated: indicating the predicate/logic expression cannot be evaluated.

Setup Frontend with Predicate Rule

Import and set up the tasympy cas.

In [1]: import truealgebra.tasympy as cas
   ...: cas.setup_func()
   ...: 

Next create a frontend with fe.postrule.rule pointing to the pedicate rule. The fe.prerule.rule is by default the donothing_rule.

In [2]:  fe = cas.create_frontend(postrule = cas.predicate_rule_bu)

Number Predicate Expressions

isnumber

The expression isnumber is a predicate function with one argument. When evaluated by the predicate rule it determines if its argument is a number or not

In [3]: fe(' isnumber(x); isnumber(2.0); isnumber(2/3); isnumber(I); isnumber(pi) ')
Ex(0):    false; true; true; true; true

As shown above, isnumber returns false when its argument is not a number. All the other predicate expressions below differ in that they are not evaluated when the predicate argument is not a number.

Next look at num below, which is a truealgebra Number object. Its value attribute is a sympy.core.mul.Mul object containing sympy numbers. The expression isnumber(num) evaluates to true.

In [4]: fe(' num := star(4, 2, pi, I) ', cas.evalnumbu)
Ex(1):    num := (8*I*pi)

In [5]: type(fe.history[-1][1].value)
Out[5]: sympy.core.mul.Mul

In [6]: fe(' isnumber(num) ')
Ex(2):    true

isrational

The expression ‘’isrational`` evaluates to true whenever its argument is an integer or a fraction.

In [7]: fe(' isrational(2.3); isrational(I); isrational(2); isrational(4/5) ')
Ex(3):    false; false; true; true

When the argument of isrational is not a number, the expression is returned unevaluated as seen below.

In [8]: fe(' isrational(x) ')
Ex(4):    isrational(x)

isinteger

The expression ‘’isinteger`` evaluates to true whenever its argument is an integer or a fraction.

In [9]: fe(' isinteger(2.3); isinteger(I); isinteger(2); isinteger(4/5) ')
Ex(5):    false; false; true; false

When the argument of isinteger is not a number, the expression is returned unevaluated as seen below.

In [10]: fe(' isinteger(x) ')
Ex(6):    isinteger(x)

isreal

The expression ‘’isreal`` evaluates to true whenever its argument is an integer or a fraction.

In [11]: fe(' isreal(2.3); isreal(I); isreal(2); isreal(4/5) ')
Ex(7):    true; false; true; true

When the argument of isreal is not a number, the expression is returned unevaluated as seen below.

In [12]: fe(' isreal(x) ')
Ex(8):    isreal(x)

iscomplex

The expression ‘’iscomplex`` evaluates to true whenever its argument is an integer or a fraction.

In [13]: fe(' iscomplex(2.3); iscomplex(I); iscomplex(2); iscomplex(4/5) ')
Ex(9):    true; true; true; true

The infinity number is not complex.

In [14]: fe(' iscomplex(oo) ')
Ex(10):    false

When the argument of iscomplex is not a number, the expression is returned unevaluated as seen below.

In [15]: fe(' iscomplex(x) ')
Ex(11):    iscomplex(x)