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 k, t
from proveit.linear_algebra import ScalarMult, TensorProd, VecAdd, VecSum
from proveit.logic import CartExp, InSet
from proveit.numbers import Complex, Exp, Interval, Mult, e, i, one, pi, subtract, two, zero
from proveit.physics.quantum import NumKet, ket0, ket1
from proveit.physics.quantum.QPE import _phase, two_pow_t

# build up the expression from sub-expressions
expr = InSet(TensorProd(VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, _phase, two_pow_t)), ket1)), VecSum(index_or_indices = [k], summand = ScalarMult(Exp(e, Mult(two, pi, i, _phase, k)), NumKet(k, t)), domain = Interval(zero, subtract(two_pow_t, one)))), CartExp(Complex, Mult(two, two_pow_t)))

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(\left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot 2^{t}} \cdot \lvert 1 \rangle\right)\right) {\otimes} \left(\sum_{k=0}^{2^{t} - 1} \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \lvert k \rangle_{t}\right)\right)\right) \in \mathbb{C}^{2 \cdot 2^{t}}

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: 32 operands: 1
1	ExprTuple	2, 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10, 11
8	Operation	operator: 12 operands: 13
9	Operation	operator: 14 operand: 19
10	Literal
11	Operation	operator: 48 operands: 16
12	Literal
13	ExprTuple	17, 18
14	Literal
15	ExprTuple	19
16	ExprTuple	62, 56
17	Operation	operator: 29 operand: 46
18	Operation	operator: 30 operands: 21
19	Lambda	parameter: 55 body: 23
20	ExprTuple	46
21	ExprTuple	24, 25
22	ExprTuple	55
23	Conditional	value: 26 condition: 27
24	Operation	operator: 58 operands: 28
25	Operation	operator: 29 operand: 64
26	Operation	operator: 30 operands: 31
27	Operation	operator: 32 operands: 33
28	ExprTuple	44, 34
29	Literal
30	Literal
31	ExprTuple	35, 36
32	Literal
33	ExprTuple	55, 37
34	Operation	operator: 48 operands: 38
35	Operation	operator: 58 operands: 39
36	Operation	operator: 40 operands: 41
37	Operation	operator: 42 operands: 43
38	ExprTuple	62, 52, 53, 54, 56
39	ExprTuple	44, 45
40	Literal
41	ExprTuple	55, 63
42	Literal
43	ExprTuple	46, 47
44	Literal
45	Operation	operator: 48 operands: 49
46	Literal
47	Operation	operator: 50 operands: 51
48	Literal
49	ExprTuple	62, 52, 53, 54, 55
50	Literal
51	ExprTuple	56, 57
52	Literal
53	Literal
54	Literal
55	Variable
56	Operation	operator: 58 operands: 59
57	Operation	operator: 60 operand: 64
58	Literal
59	ExprTuple	62, 63
60	Literal
61	ExprTuple	64
62	Literal
63	Variable
64	Literal