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, Exp(two, subtract(frac(Add(t, one), two), frac(t, two))))
sub_expr3 = VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, _phase, two_pow_t)), ket1))
sub_expr4 = 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 = ExprTuple(TensorProd(ScalarMult(sub_expr2, sub_expr3), TensorProd(sub_expr4)), ScalarMult(sub_expr2, TensorProd(sub_expr3, sub_expr4)))

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}{2^{\frac{t + 1}{2} - \frac{t}{2}}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot 2^{t}} \cdot \lvert 1 \rangle\right)\right)\right) {\otimes} \left(\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: 10 operands: 3
2	Operation	operator: 48 operands: 4
3	ExprTuple	5, 6
4	ExprTuple	12, 7
5	Operation	operator: 48 operands: 8
6	Operation	operator: 10 operands: 9
7	Operation	operator: 10 operands: 11
8	ExprTuple	12, 13
9	ExprTuple	14
10	Literal
11	ExprTuple	13, 14
12	Operation	operator: 61 operands: 15
13	Operation	operator: 35 operands: 16
14	ExprRange	lambda_map: 17 start_index: 18 end_index: 54
15	ExprTuple	69, 19
16	ExprTuple	41, 20
17	Lambda	parameter: 82 body: 21
18	Operation	operator: 57 operands: 22
19	Operation	operator: 76 operands: 23
20	Operation	operator: 48 operands: 24
21	Operation	operator: 48 operands: 25
22	ExprTuple	26, 69
23	ExprTuple	78, 27
24	ExprTuple	28, 56
25	ExprTuple	29, 30
26	Operation	operator: 80 operand: 66
27	Operation	operator: 57 operands: 32
28	Operation	operator: 76 operands: 33
29	Operation	operator: 61 operands: 34
30	Operation	operator: 35 operands: 36
31	ExprTuple	66
32	ExprTuple	37, 38
33	ExprTuple	67, 39
34	ExprTuple	69, 40
35	Literal
36	ExprTuple	41, 42
37	Operation	operator: 61 operands: 43
38	Operation	operator: 80 operand: 51
39	Operation	operator: 70 operands: 45
40	Operation	operator: 76 operands: 46
41	Operation	operator: 64 operand: 54
42	Operation	operator: 48 operands: 49
43	ExprTuple	50, 78
44	ExprTuple	51
45	ExprTuple	78, 72, 73, 75, 52
46	ExprTuple	78, 53
47	ExprTuple	54
48	Literal
49	ExprTuple	55, 56
50	Operation	operator: 57 operands: 58
51	Operation	operator: 61 operands: 59
52	Operation	operator: 76 operands: 60
53	Operation	operator: 61 operands: 62
54	Literal
55	Operation	operator: 76 operands: 63
56	Operation	operator: 64 operand: 69
57	Literal
58	ExprTuple	66, 69
59	ExprTuple	66, 78
60	ExprTuple	78, 66
61	Literal
62	ExprTuple	69, 78
63	ExprTuple	67, 68
64	Literal
65	ExprTuple	69
66	Variable
67	Literal
68	Operation	operator: 70 operands: 71
69	Literal
70	Literal
71	ExprTuple	78, 72, 73, 74, 75
72	Literal
73	Literal
74	Operation	operator: 76 operands: 77
75	Literal
76	Literal
77	ExprTuple	78, 79
78	Literal
79	Operation	operator: 80 operand: 82
80	Literal
81	ExprTuple	82
82	Variable