Expression of type VecSum

from the theory of proveit.physics.quantum.QPE

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 k, t
from proveit.linear_algebra import ScalarMult, VecSum
from proveit.numbers import Add, Exp, Interval, Mult, e, i, one, pi, subtract, two
from proveit.physics.quantum import NumKet
from proveit.physics.quantum.QPE import _phase, two_pow_t

# build up the expression from sub-expressions
expr = VecSum(index_or_indices = [k], summand = ScalarMult(Exp(e, Mult(two, pi, i, _phase, k)), NumKet(k, Add(t, one))), domain = Interval(two_pow_t, subtract(Mult(two, two_pow_t), one)))

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())

\sum_{k=2^{t}}^{\left(2 \cdot 2^{t}\right) - 1} \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \lvert k \rangle_{t + 1}\right)

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

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