Expression of type ExprTuple

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 ExprRange, ExprTuple, Variable, t
from proveit.core_expr_types import Len
from proveit.linear_algebra import ScalarMult, TensorProd, VecAdd
from proveit.numbers import Add, Exp, Mult, Neg, e, frac, i, one, pi, sqrt, two, zero
from proveit.physics.quantum import ket0, ket1
from proveit.physics.quantum.QPE import _phase, two_pow_t

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = frac(one, sqrt(two))
expr = ExprTuple(Len(operands = [sub_expr2, TensorProd(VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, two_pow_t, _phase)), ket1)), ExprRange(sub_expr1, ScalarMult(sub_expr2, VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(sub_expr1)), _phase)), ket1))), Add(Neg(t), one), zero).with_decreasing_order())]), Len(operands = [ExprRange(sub_expr1, sub_expr1, one, two)]))

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(\frac{1}{\sqrt{2}}, \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{t} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right){\otimes} \left(\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{t - 1} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)\right) {\otimes}  \left(\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{t - 2} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)\right) {\otimes}  \ldots {\otimes}  \left(\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{0} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)\right)\right)|, |\left(1, \ldots, 2\right)|\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Operation	operator: 4 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	24, 6
4	Literal
5	ExprTuple	7
6	Operation	operator: 8 operands: 9
7	ExprRange	lambda_map: 10 start_index: 54 end_index: 63
8	Literal
9	ExprTuple	11, 12
10	Lambda	parameter: 67 body: 67
11	Operation	operator: 29 operands: 13
12	ExprRange	lambda_map: 14 start_index: 15 end_index: 42
13	ExprTuple	33, 16
14	Lambda	parameter: 67 body: 17
15	Operation	operator: 18 operands: 19
16	Operation	operator: 38 operands: 20
17	Operation	operator: 38 operands: 21
18	Literal
19	ExprTuple	22, 54
20	ExprTuple	23, 44
21	ExprTuple	24, 25
22	Operation	operator: 65 operand: 51
23	Operation	operator: 61 operands: 27
24	Operation	operator: 46 operands: 28
25	Operation	operator: 29 operands: 30
26	ExprTuple	51
27	ExprTuple	52, 31
28	ExprTuple	54, 32
29	Literal
30	ExprTuple	33, 34
31	Operation	operator: 55 operands: 35
32	Operation	operator: 61 operands: 36
33	Operation	operator: 49 operand: 42
34	Operation	operator: 38 operands: 39
35	ExprTuple	63, 57, 58, 40, 60
36	ExprTuple	63, 41
37	ExprTuple	42
38	Literal
39	ExprTuple	43, 44
40	Operation	operator: 61 operands: 45
41	Operation	operator: 46 operands: 47
42	Literal
43	Operation	operator: 61 operands: 48
44	Operation	operator: 49 operand: 54
45	ExprTuple	63, 51
46	Literal
47	ExprTuple	54, 63
48	ExprTuple	52, 53
49	Literal
50	ExprTuple	54
51	Variable
52	Literal
53	Operation	operator: 55 operands: 56
54	Literal
55	Literal
56	ExprTuple	63, 57, 58, 59, 60
57	Literal
58	Literal
59	Operation	operator: 61 operands: 62
60	Literal
61	Literal
62	ExprTuple	63, 64
63	Literal
64	Operation	operator: 65 operand: 67
65	Literal
66	ExprTuple	67
67	Variable