Expression of type VecAdd

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 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
expr = VecAdd(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())

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)

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

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