Expression of type Equals

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
from proveit.linear_algebra import ScalarMult, VecSum
from proveit.logic import Equals
from proveit.numbers import Exp, Interval, Mult, e, frac, i, one, pi, sqrt, two, zero
from proveit.physics.quantum import Ket
from proveit.physics.quantum.QPE import SubIndexed, _phase, _psi

# build up the expression from sub-expressions
expr = Equals(SubIndexed(_psi, [one]), ScalarMult(frac(one, sqrt(two)), VecSum(index_or_indices = [k], summand = ScalarMult(Exp(e, Mult(two, pi, i, _phase, k)), Ket(k)), domain = Interval(zero, 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())

\lvert \psi_{1} \rangle = \left(\frac{1}{\sqrt{2}} \cdot \left(\sum_{k=0}^{1} \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \lvert k \rangle\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',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# 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: 5 operand: 38
4	Operation	operator: 22 operands: 7
5	Literal
6	ExprTuple	38
7	ExprTuple	8, 9
8	Operation	operator: 20 operands: 10
9	Operation	operator: 11 operand: 14
10	ExprTuple	38, 13
11	Literal
12	ExprTuple	14
13	Operation	operator: 29 operands: 15
14	Lambda	parameter: 45 body: 16
15	ExprTuple	41, 17
16	Conditional	value: 18 condition: 19
17	Operation	operator: 20 operands: 21
18	Operation	operator: 22 operands: 23
19	Operation	operator: 24 operands: 25
20	Literal
21	ExprTuple	38, 41
22	Literal
23	ExprTuple	26, 27
24	Literal
25	ExprTuple	45, 28
26	Operation	operator: 29 operands: 30
27	Operation	operator: 31 operand: 45
28	Operation	operator: 33 operands: 34
29	Literal
30	ExprTuple	35, 36
31	Literal
32	ExprTuple	45
33	Literal
34	ExprTuple	37, 38
35	Literal
36	Operation	operator: 39 operands: 40
37	Literal
38	Literal
39	Literal
40	ExprTuple	41, 42, 43, 44, 45
41	Literal
42	Literal
43	Literal
44	Literal
45	Variable