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, VecSum
from proveit.numbers import Exp, Interval, Mult, e, i, one, pi, two, zero

# build up the expression from sub-expressions
expr = ExprTuple(Function(v, [zero]), VecSum(index_or_indices = [k], summand = ScalarMult(Exp(e, Mult(two, pi, i, k)), vk), 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(v\left(0\right), \sum_{k=1}^{N} \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot k} \cdot v\left(k\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: 20 operand: 6
2	Operation	operator: 4 operand: 7
3	ExprTuple	6
4	Literal
5	ExprTuple	7
6	Literal
7	Lambda	parameter: 33 body: 8
8	Conditional	value: 9 condition: 10
9	Operation	operator: 11 operands: 12
10	Operation	operator: 13 operands: 14
11	Literal
12	ExprTuple	15, 16
13	Literal
14	ExprTuple	33, 17
15	Operation	operator: 18 operands: 19
16	Operation	operator: 20 operand: 33
17	Operation	operator: 22 operands: 23
18	Literal
19	ExprTuple	24, 25
20	Variable
21	ExprTuple	33
22	Literal
23	ExprTuple	26, 27
24	Literal
25	Operation	operator: 28 operands: 29
26	Literal
27	Variable
28	Literal
29	ExprTuple	30, 31, 32, 33
30	Literal
31	Literal
32	Literal
33	Variable