# from the theory of proveit.numbers.division¶

In [1]:
import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
# import Expression classes needed to build the expression
from proveit import Conditional, Lambda, a, b
from proveit.logic import And, InSet, NotEquals
from proveit.numbers import Complex, frac, zero

In [2]:
# build up the expression from sub-expressions
expr = Lambda([a, b], Conditional(InSet(frac(a, b), Complex), And(InSet(a, Complex), InSet(b, Complex), NotEquals(b, zero))))

expr:
In [3]:
# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(a, b\right) \mapsto \left\{\frac{a}{b} \in \mathbb{C} \textrm{ if } a \in \mathbb{C} ,  b \in \mathbb{C} ,  b \neq 0\right..

In [5]:
stored_expr.style_options()

no style options
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Lambdaparameters: 12
body: 1
1Conditionalvalue: 2
condition: 3
2Operationoperator: 14
operands: 4
3Operationoperator: 5
operands: 6
4ExprTuple7, 19
5Literal
6ExprTuple8, 9, 10
7Operationoperator: 11
operands: 12
8Operationoperator: 14
operands: 13
9Operationoperator: 14
operands: 15
10Operationoperator: 16
operands: 17
11Literal
12ExprTuple18, 20
13ExprTuple18, 19
14Literal
15ExprTuple20, 19
16Literal
17ExprTuple20, 21
18Variable
19Literal
20Variable
21Literal