# from the theory of proveit.numbers.modular¶

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, N, x
from proveit.logic import And, Equals, InSet
from proveit.numbers import Abs, LessEq, ModAbs, Real, RealPos, frac, two

In [2]:
# build up the expression from sub-expressions
sub_expr1 = Abs(x)
expr = Lambda([x, N], Conditional(Equals(ModAbs(x, N), sub_expr1), And(InSet(x, Real), InSet(N, RealPos), LessEq(sub_expr1, frac(N, two)))))

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(x, N\right) \mapsto \left\{\left|x\right|_{\textup{mod}\thinspace N} = \left|x\right| \textrm{ if } x \in \mathbb{R} ,  N \in \mathbb{R}^+ ,  \left|x\right| \leq \frac{N}{2}\right..

In [5]:
stored_expr.style_options()

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

core typesub-expressionsexpression
0Lambdaparameters: 13
body: 1
1Conditionalvalue: 2
condition: 3
2Operationoperator: 4
operands: 5
3Operationoperator: 6
operands: 7
4Literal
5ExprTuple8, 21
6Literal
7ExprTuple9, 10, 11
8Operationoperator: 12
operands: 13
9Operationoperator: 15
operands: 14
10Operationoperator: 15
operands: 16
11Operationoperator: 17
operands: 18
12Literal
13ExprTuple27, 28
14ExprTuple27, 19
15Literal
16ExprTuple28, 20
17Literal
18ExprTuple21, 22
19Literal
20Literal
21Operationoperator: 23
operand: 27
22Operationoperator: 25
operands: 26
23Literal
24ExprTuple27
25Literal
26ExprTuple28, 29
27Variable
28Variable
29Literal