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}")
sub_expr2 = frac(one, sqrt(two))
sub_expr3 = 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()
expr = ExprTuple(ScalarMult(sub_expr2, TensorProd(VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, two_pow_t, _phase)), ket1)), sub_expr3)), ScalarMult(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)), sub_expr3)))

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(\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), \frac{1}{2^{\frac{t + 1}{2} - \frac{t}{2}}} \cdot \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(\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)\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: 59 operands: 3
2	Operation	operator: 59 operands: 4
3	ExprTuple	35, 5
4	ExprTuple	6, 7
5	Operation	operator: 10 operands: 8
6	Operation	operator: 67 operands: 9
7	Operation	operator: 10 operands: 11
8	ExprTuple	12, 15
9	ExprTuple	75, 13
10	Literal
11	ExprTuple	14, 15
12	Operation	operator: 43 operands: 16
13	Operation	operator: 82 operands: 17
14	Operation	operator: 43 operands: 18
15	ExprRange	lambda_map: 19 start_index: 20 end_index: 63
16	ExprTuple	50, 21
17	ExprTuple	84, 22
18	ExprTuple	50, 23
19	Lambda	parameter: 88 body: 24
20	Operation	operator: 53 operands: 25
21	Operation	operator: 59 operands: 26
22	Operation	operator: 53 operands: 27
23	Operation	operator: 59 operands: 28
24	Operation	operator: 59 operands: 29
25	ExprTuple	30, 75
26	ExprTuple	31, 65
27	ExprTuple	32, 33
28	ExprTuple	34, 65
29	ExprTuple	35, 36
30	Operation	operator: 86 operand: 72
31	Operation	operator: 82 operands: 38
32	Operation	operator: 67 operands: 39
33	Operation	operator: 86 operand: 47
34	Operation	operator: 82 operands: 41
35	Operation	operator: 67 operands: 42
36	Operation	operator: 43 operands: 44
37	ExprTuple	72
38	ExprTuple	73, 45
39	ExprTuple	46, 84
40	ExprTuple	47
41	ExprTuple	73, 48
42	ExprTuple	75, 49
43	Literal
44	ExprTuple	50, 51
45	Operation	operator: 76 operands: 52
46	Operation	operator: 53 operands: 54
47	Operation	operator: 67 operands: 55
48	Operation	operator: 76 operands: 56
49	Operation	operator: 82 operands: 57
50	Operation	operator: 70 operand: 63
51	Operation	operator: 59 operands: 60
52	ExprTuple	84, 78, 79, 61, 81
53	Literal
54	ExprTuple	72, 75
55	ExprTuple	72, 84
56	ExprTuple	84, 78, 79, 81, 61
57	ExprTuple	84, 62
58	ExprTuple	63
59	Literal
60	ExprTuple	64, 65
61	Operation	operator: 82 operands: 66
62	Operation	operator: 67 operands: 68
63	Literal
64	Operation	operator: 82 operands: 69
65	Operation	operator: 70 operand: 75
66	ExprTuple	84, 72
67	Literal
68	ExprTuple	75, 84
69	ExprTuple	73, 74
70	Literal
71	ExprTuple	75
72	Variable
73	Literal
74	Operation	operator: 76 operands: 77
75	Literal
76	Literal
77	ExprTuple	84, 78, 79, 80, 81
78	Literal
79	Literal
80	Operation	operator: 82 operands: 83
81	Literal
82	Literal
83	ExprTuple	84, 85
84	Literal
85	Operation	operator: 86 operand: 88
86	Literal
87	ExprTuple	88
88	Variable