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 = Add(sub_expr2, one)
sub_expr4 = frac(one, sqrt(two))
sub_expr5 = ScalarMult(sub_expr4, VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(sub_expr1)), _phase)), ket1)))
expr = ExprTuple([ScalarMult(sub_expr4, VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(sub_expr3)), _phase)), ket1))), ExprRange(sub_expr1, sub_expr5, Add(sub_expr2, two), zero).with_decreasing_order(), _ket_u], [ExprRange(sub_expr1, sub_expr5, sub_expr3, 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(\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), \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), \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), \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)\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, 4, 6
2	ExprTuple	5, 6
3	Operation	operator: 29 operands: 7
4	ExprRange	lambda_map: 9 start_index: 8 end_index: 33
5	ExprRange	lambda_map: 9 start_index: 56 end_index: 33
6	Literal
7	ExprTuple	16, 10
8	Operation	operator: 59 operands: 11
9	Lambda	parameter: 64 body: 12
10	Operation	operator: 20 operands: 13
11	ExprTuple	62, 57
12	Operation	operator: 29 operands: 14
13	ExprTuple	24, 15
14	ExprTuple	16, 17
15	Operation	operator: 29 operands: 18
16	Operation	operator: 37 operands: 19
17	Operation	operator: 20 operands: 21
18	ExprTuple	22, 35
19	ExprTuple	63, 23
20	Literal
21	ExprTuple	24, 25
22	Operation	operator: 54 operands: 26
23	Operation	operator: 54 operands: 27
24	Operation	operator: 40 operand: 33
25	Operation	operator: 29 operands: 30
26	ExprTuple	43, 31
27	ExprTuple	57, 32
28	ExprTuple	33
29	Literal
30	ExprTuple	34, 35
31	Operation	operator: 46 operands: 36
32	Operation	operator: 37 operands: 38
33	Literal
34	Operation	operator: 54 operands: 39
35	Operation	operator: 40 operand: 63
36	ExprTuple	57, 49, 50, 42, 52
37	Literal
38	ExprTuple	63, 57
39	ExprTuple	43, 44
40	Literal
41	ExprTuple	63
42	Operation	operator: 54 operands: 45
43	Literal
44	Operation	operator: 46 operands: 47
45	ExprTuple	57, 48
46	Literal
47	ExprTuple	57, 49, 50, 51, 52
48	Operation	operator: 65 operand: 56
49	Literal
50	Literal
51	Operation	operator: 54 operands: 55
52	Literal
53	ExprTuple	56
54	Literal
55	ExprTuple	57, 58
56	Operation	operator: 59 operands: 60
57	Literal
58	Operation	operator: 65 operand: 64
59	Literal
60	ExprTuple	62, 63
61	ExprTuple	64
62	Operation	operator: 65 operand: 67
63	Literal
64	Variable
65	Literal
66	ExprTuple	67
67	Variable