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, 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 = Neg(t)
sub_expr3 = frac(one, sqrt(two))
sub_expr4 = ScalarMult(sub_expr3, VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(sub_expr1)), _phase)), ket1)))
expr = ExprTuple([ExprRange(sub_expr1, sub_expr4, sub_expr2, zero)], [ScalarMult(sub_expr3, VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, two_pow_t, _phase)), ket1))), ExprRange(sub_expr1, sub_expr4, Add(sub_expr2, one), zero)])

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