# 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, 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 = 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\{\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()

namedescriptiondefaultcurrent valuerelated methods
condition_delimiter'comma' or 'and'commacomma('with_comma_delimiter', 'with_conjunction_delimiter')
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Conditionalvalue: 1
condition: 2
1Operationoperator: 13
operands: 3
2Operationoperator: 4
operands: 5
3ExprTuple6, 18
4Literal
5ExprTuple7, 8, 9
6Operationoperator: 10
operands: 11
7Operationoperator: 13
operands: 12
8Operationoperator: 13
operands: 14
9Operationoperator: 15
operands: 16
10Literal
11ExprTuple17, 19
12ExprTuple17, 18
13Literal
14ExprTuple19, 18
15Literal
16ExprTuple19, 20
17Variable
18Literal
19Variable
20Literal