Expression of type Conditional

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, N, k, vk
from proveit.linear_algebra import ScalarMult
from proveit.logic import InSet
from proveit.numbers import Exp, Interval, Mult, e, i, one, pi, two

# build up the expression from sub-expressions
expr = Conditional(ScalarMult(Exp(e, Mult(two, pi, i, k)), vk), InSet(k, Interval(one, 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\{\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot k} \cdot v\left(k\right) \textrm{ if } k \in \{1~\ldotp \ldotp~N\}\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

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