Expression of type ExprTuple

from the theory of proveit.linear_algebra.addition

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.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, ExprTuple, Lambda, N, k, vk
from proveit.linear_algebra import ScalarMult
from proveit.logic import InSet
from proveit.numbers import Exp, Interval, Mult, e, i, pi, two, zero

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(k, Conditional(ScalarMult(Exp(e, Mult(two, pi, i, k)), vk), InSet(k, Interval(zero, N)))))

expr:

# 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

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(k \mapsto \left\{\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot k} \cdot v\left(k\right) \textrm{ if } k \in \{0~\ldotp \ldotp~N\}\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 27 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	27, 11
9	Operation	operator: 12 operands: 13
10	Operation	operator: 14 operand: 27
11	Operation	operator: 16 operands: 17
12	Literal
13	ExprTuple	18, 19
14	Variable
15	ExprTuple	27
16	Literal
17	ExprTuple	20, 21
18	Literal
19	Operation	operator: 22 operands: 23
20	Literal
21	Variable
22	Literal
23	ExprTuple	24, 25, 26, 27
24	Literal
25	Literal
26	Literal
27	Variable