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 ExprTuple, Function, N, k, v, vk
from proveit.linear_algebra import ScalarMult, VecAdd, VecSum
from proveit.numbers import Exp, Interval, Mult, e, i, one, pi, two, zero

# build up the expression from sub-expressions
sub_expr1 = [k]
sub_expr2 = ScalarMult(Exp(e, Mult(two, pi, i, k)), vk)
expr = ExprTuple(VecSum(index_or_indices = sub_expr1, summand = sub_expr2, domain = Interval(zero, N)), VecAdd(Function(v, [zero]), VecSum(index_or_indices = sub_expr1, summand = sub_expr2, domain = 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(\sum_{k=0}^{N} \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot k} \cdot v\left(k\right)\right), v\left(0\right) + \left(\sum_{k=1}^{N} \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot k} \cdot v\left(k\right)\right)\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Operation	operator: 11 operand: 6
2	Operation	operator: 4 operands: 5
3	ExprTuple	6
4	Literal
5	ExprTuple	7, 8
6	Lambda	parameter: 44 body: 9
7	Operation	operator: 31 operand: 25
8	Operation	operator: 11 operand: 14
9	Conditional	value: 18 condition: 13
10	ExprTuple	25
11	Literal
12	ExprTuple	14
13	Operation	operator: 23 operands: 15
14	Lambda	parameter: 44 body: 16
15	ExprTuple	44, 17
16	Conditional	value: 18 condition: 19
17	Operation	operator: 33 operands: 20
18	Operation	operator: 21 operands: 22
19	Operation	operator: 23 operands: 24
20	ExprTuple	25, 38
21	Literal
22	ExprTuple	26, 27
23	Literal
24	ExprTuple	44, 28
25	Literal
26	Operation	operator: 29 operands: 30
27	Operation	operator: 31 operand: 44
28	Operation	operator: 33 operands: 34
29	Literal
30	ExprTuple	35, 36
31	Variable
32	ExprTuple	44
33	Literal
34	ExprTuple	37, 38
35	Literal
36	Operation	operator: 39 operands: 40
37	Literal
38	Variable
39	Literal
40	ExprTuple	41, 42, 43, 44
41	Literal
42	Literal
43	Literal
44	Variable