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 SubIndexed, _phase, _psi, two_pow_t

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Add(t, one)
expr = ExprTuple(ScalarMult(frac(one, Exp(two, subtract(frac(sub_expr2, 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())), SubIndexed(_psi, [sub_expr2]))

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