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 ExprTuple, Lambda, Variable, t
from proveit.linear_algebra import ScalarMult, VecAdd
from proveit.numbers import Add, Exp, Mult, Neg, e, frac, i, one, pi, sqrt, two
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("_b", latex_format = r"{_{-}b}")
sub_expr2 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr3 = frac(one, sqrt(two))
expr = ExprTuple(Lambda(sub_expr1, ScalarMult(sub_expr3, VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(Add(Neg(t), one))), _phase)), ket1)))), Lambda(sub_expr2, ScalarMult(sub_expr3, VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(sub_expr2)), _phase)), ket1)))), Lambda(sub_expr1, _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({_{-}b} \mapsto \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), {_{-}a} \mapsto \left(\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{-{_{-}a}} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)\right), {_{-}b} \mapsto \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	Lambda	parameter: 10 body: 4
2	Lambda	parameter: 58 body: 5
3	Lambda	parameter: 10 body: 7
4	Operation	operator: 25 operands: 8
5	Operation	operator: 25 operands: 9
6	ExprTuple	10
7	Literal
8	ExprTuple	12, 11
9	ExprTuple	12, 13
10	Variable
11	Operation	operator: 16 operands: 14
12	Operation	operator: 33 operands: 15
13	Operation	operator: 16 operands: 17
14	ExprTuple	20, 18
15	ExprTuple	62, 19
16	Literal
17	ExprTuple	20, 21
18	Operation	operator: 25 operands: 22
19	Operation	operator: 50 operands: 23
20	Operation	operator: 36 operand: 29
21	Operation	operator: 25 operands: 26
22	ExprTuple	27, 31
23	ExprTuple	53, 28
24	ExprTuple	29
25	Literal
26	ExprTuple	30, 31
27	Operation	operator: 50 operands: 32
28	Operation	operator: 33 operands: 34
29	Literal
30	Operation	operator: 50 operands: 35
31	Operation	operator: 36 operand: 62
32	ExprTuple	39, 38
33	Literal
34	ExprTuple	62, 53
35	ExprTuple	39, 40
36	Literal
37	ExprTuple	62
38	Operation	operator: 42 operands: 41
39	Literal
40	Operation	operator: 42 operands: 43
41	ExprTuple	53, 45, 46, 44, 48
42	Literal
43	ExprTuple	53, 45, 46, 47, 48
44	Operation	operator: 50 operands: 49
45	Literal
46	Literal
47	Operation	operator: 50 operands: 51
48	Literal
49	ExprTuple	53, 52
50	Literal
51	ExprTuple	53, 54
52	Operation	operator: 63 operand: 57
53	Literal
54	Operation	operator: 63 operand: 58
55	ExprTuple	57
56	ExprTuple	58
57	Operation	operator: 59 operands: 60
58	Variable
59	Literal
60	ExprTuple	61, 62
61	Operation	operator: 63 operand: 65
62	Literal
63	Literal
64	ExprTuple	65
65	Variable