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 _ket_u, _phase

# 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))
expr = ExprTuple(ScalarMult(sub_expr3, VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(Add(sub_expr2, one))), _phase)), ket1))), ExprRange(sub_expr1, ScalarMult(sub_expr3, VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(sub_expr1)), _phase)), ket1))), Add(sub_expr2, two), zero).with_decreasing_order(), _ket_u)

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