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.linear_algebra import ScalarMult, TensorProd, VecAdd
from proveit.numbers import Add, Exp, Mult, Neg, e, frac, i, one, pi, sqrt, subtract, 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}")
expr = ExprTuple(frac(one, Exp(two, subtract(frac(Add(t, one), two), frac(t, two)))), TensorProd(VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, _phase, two_pow_t)), ket1)), ExprRange(sub_expr1, ScalarMult(frac(one, sqrt(two)), VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(sub_expr1)), _phase)), ket1))), Add(Neg(t), one), zero).with_decreasing_order()))

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}{2^{\frac{t + 1}{2} - \frac{t}{2}}}, \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(\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)

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: 53 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	61, 6
4	Literal
5	ExprTuple	7, 8
6	Operation	operator: 68 operands: 9
7	Operation	operator: 31 operands: 10
8	ExprRange	lambda_map: 11 start_index: 12 end_index: 49
9	ExprTuple	70, 13
10	ExprTuple	37, 14
11	Lambda	parameter: 74 body: 15
12	Operation	operator: 39 operands: 16
13	Operation	operator: 39 operands: 17
14	Operation	operator: 45 operands: 18
15	Operation	operator: 45 operands: 19
16	ExprTuple	20, 61
17	ExprTuple	21, 22
18	ExprTuple	23, 51
19	ExprTuple	24, 25
20	Operation	operator: 72 operand: 58
21	Operation	operator: 53 operands: 27
22	Operation	operator: 72 operand: 34
23	Operation	operator: 68 operands: 29
24	Operation	operator: 53 operands: 30
25	Operation	operator: 31 operands: 32
26	ExprTuple	58
27	ExprTuple	33, 70
28	ExprTuple	34
29	ExprTuple	59, 35
30	ExprTuple	61, 36
31	Literal
32	ExprTuple	37, 38
33	Operation	operator: 39 operands: 40
34	Operation	operator: 53 operands: 41
35	Operation	operator: 62 operands: 42
36	Operation	operator: 68 operands: 43
37	Operation	operator: 56 operand: 49
38	Operation	operator: 45 operands: 46
39	Literal
40	ExprTuple	58, 61
41	ExprTuple	58, 70
42	ExprTuple	70, 64, 65, 67, 47
43	ExprTuple	70, 48
44	ExprTuple	49
45	Literal
46	ExprTuple	50, 51
47	Operation	operator: 68 operands: 52
48	Operation	operator: 53 operands: 54
49	Literal
50	Operation	operator: 68 operands: 55
51	Operation	operator: 56 operand: 61
52	ExprTuple	70, 58
53	Literal
54	ExprTuple	61, 70
55	ExprTuple	59, 60
56	Literal
57	ExprTuple	61
58	Variable
59	Literal
60	Operation	operator: 62 operands: 63
61	Literal
62	Literal
63	ExprTuple	70, 64, 65, 66, 67
64	Literal
65	Literal
66	Operation	operator: 68 operands: 69
67	Literal
68	Literal
69	ExprTuple	70, 71
70	Literal
71	Operation	operator: 72 operand: 74
72	Literal
73	ExprTuple	74
74	Variable