Expression of type InSet

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 Variable, t
from proveit.linear_algebra import ScalarMult, VecAdd
from proveit.logic import InSet
from proveit.numbers import Add, Exp, Mult, Neg, e, frac, i, one, pi, sqrt, two
from proveit.physics.quantum import ket0, ket1
from proveit.physics.quantum.QPE import _phase

# build up the expression from sub-expressions
expr = InSet(ScalarMult(frac(one, sqrt(two)), VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(Add(Neg(t), one))), _phase)), ket1))), Variable("_a", latex_format = r"{_{-}a}"))

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(\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{-\left(-t + 1\right)} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)\right) \in {_{-}a}

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: 16 operands: 5
4	Variable
5	ExprTuple	6, 7
6	Operation	operator: 22 operands: 8
7	Operation	operator: 9 operands: 10
8	ExprTuple	44, 11
9	Literal
10	ExprTuple	12, 13
11	Operation	operator: 35 operands: 14
12	Operation	operator: 25 operand: 19
13	Operation	operator: 16 operands: 17
14	ExprTuple	37, 18
15	ExprTuple	19
16	Literal
17	ExprTuple	20, 21
18	Operation	operator: 22 operands: 23
19	Literal
20	Operation	operator: 35 operands: 24
21	Operation	operator: 25 operand: 44
22	Literal
23	ExprTuple	44, 37
24	ExprTuple	27, 28
25	Literal
26	ExprTuple	44
27	Literal
28	Operation	operator: 29 operands: 30
29	Literal
30	ExprTuple	37, 31, 32, 33, 34
31	Literal
32	Literal
33	Operation	operator: 35 operands: 36
34	Literal
35	Literal
36	ExprTuple	37, 38
37	Literal
38	Operation	operator: 45 operand: 40
39	ExprTuple	40
40	Operation	operator: 41 operands: 42
41	Literal
42	ExprTuple	43, 44
43	Operation	operator: 45 operand: 47
44	Literal
45	Literal
46	ExprTuple	47
47	Variable