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, TensorProd, VecSum
from proveit.numbers import Exp, Interval, Mult, e, i, one, pi, subtract, two, zero
from proveit.physics.quantum import NumKet, ket1
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(Mult(Exp(e, Mult(two, pi, i, _phase, two_pow_t)), Exp(e, Mult(two, pi, i, _phase, k))), TensorProd(ket1, NumKet(k, t))), domain = Interval(zero, subtract(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=0}^{2^{t} - 1} \left(\left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot 2^{t}} \cdot \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k}\right) \cdot \left(\lvert 1 \rangle {\otimes} \lvert k \rangle_{t}\right)\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: 46 body: 5
4	ExprTuple	46
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	46, 14
12	Operation	operator: 38 operands: 15
13	Operation	operator: 16 operands: 17
14	Operation	operator: 18 operands: 19
15	ExprTuple	20, 21
16	Literal
17	ExprTuple	22, 23
18	Literal
19	ExprTuple	24, 25
20	Operation	operator: 48 operands: 26
21	Operation	operator: 48 operands: 27
22	Operation	operator: 28 operand: 47
23	Operation	operator: 29 operands: 30
24	Literal
25	Operation	operator: 31 operands: 32
26	ExprTuple	34, 33
27	ExprTuple	34, 35
28	Literal
29	Literal
30	ExprTuple	46, 51
31	Literal
32	ExprTuple	42, 36
33	Operation	operator: 38 operands: 37
34	Literal
35	Operation	operator: 38 operands: 39
36	Operation	operator: 40 operand: 47
37	ExprTuple	50, 43, 44, 45, 42
38	Literal
39	ExprTuple	50, 43, 44, 45, 46
40	Literal
41	ExprTuple	47
42	Operation	operator: 48 operands: 49
43	Literal
44	Literal
45	Literal
46	Variable
47	Literal
48	Literal
49	ExprTuple	50, 51
50	Literal
51	Variable