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 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 QubitSpace, 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))), QubitSpace)

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 \mathbb{C}^{2}

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: 19 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10, 40
8	Operation	operator: 25 operands: 11
9	Operation	operator: 12 operands: 13
10	Literal
11	ExprTuple	47, 14
12	Literal
13	ExprTuple	15, 16
14	Operation	operator: 38 operands: 17
15	Operation	operator: 28 operand: 22
16	Operation	operator: 19 operands: 20
17	ExprTuple	40, 21
18	ExprTuple	22
19	Literal
20	ExprTuple	23, 24
21	Operation	operator: 25 operands: 26
22	Literal
23	Operation	operator: 38 operands: 27
24	Operation	operator: 28 operand: 47
25	Literal
26	ExprTuple	47, 40
27	ExprTuple	30, 31
28	Literal
29	ExprTuple	47
30	Literal
31	Operation	operator: 32 operands: 33
32	Literal
33	ExprTuple	40, 34, 35, 36, 37
34	Literal
35	Literal
36	Operation	operator: 38 operands: 39
37	Literal
38	Literal
39	ExprTuple	40, 41
40	Literal
41	Operation	operator: 48 operand: 43
42	ExprTuple	43
43	Operation	operator: 44 operands: 45
44	Literal
45	ExprTuple	46, 47
46	Operation	operator: 48 operand: 50
47	Literal
48	Literal
49	ExprTuple	50
50	Variable