# 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, ExprTuple, 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 = ExprTuple(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(\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..\right)

In [5]:
stored_expr.style_options()

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

core typesub-expressionsexpression
0ExprTuple1
1Lambdaparameters: 14
body: 2
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operands: 6
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple9, 22
7Literal
8ExprTuple10, 11, 12
9Operationoperator: 13
operands: 14
10Operationoperator: 16
operands: 15
11Operationoperator: 16
operands: 17
12Operationoperator: 18
operands: 19
13Literal
14ExprTuple28, 29
15ExprTuple28, 20
16Literal
17ExprTuple29, 21
18Literal
19ExprTuple22, 23
20Literal
21Literal
22Operationoperator: 24
operand: 28
23Operationoperator: 26
operands: 27
24Literal
25ExprTuple28
26Literal
27ExprTuple29, 30
28Variable
29Variable
30Literal