Expression of type Len

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 Lambda, Variable, t
from proveit.core_expr_types import Len
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 = Len(operands = [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
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4, 5
3	Lambda	parameter: 12 body: 6
4	Lambda	parameter: 60 body: 7
5	Lambda	parameter: 12 body: 9
6	Operation	operator: 27 operands: 10
7	Operation	operator: 27 operands: 11
8	ExprTuple	12
9	Literal
10	ExprTuple	14, 13
11	ExprTuple	14, 15
12	Variable
13	Operation	operator: 18 operands: 16
14	Operation	operator: 35 operands: 17
15	Operation	operator: 18 operands: 19
16	ExprTuple	22, 20
17	ExprTuple	64, 21
18	Literal
19	ExprTuple	22, 23
20	Operation	operator: 27 operands: 24
21	Operation	operator: 52 operands: 25
22	Operation	operator: 38 operand: 31
23	Operation	operator: 27 operands: 28
24	ExprTuple	29, 33
25	ExprTuple	55, 30
26	ExprTuple	31
27	Literal
28	ExprTuple	32, 33
29	Operation	operator: 52 operands: 34
30	Operation	operator: 35 operands: 36
31	Literal
32	Operation	operator: 52 operands: 37
33	Operation	operator: 38 operand: 64
34	ExprTuple	41, 40
35	Literal
36	ExprTuple	64, 55
37	ExprTuple	41, 42
38	Literal
39	ExprTuple	64
40	Operation	operator: 44 operands: 43
41	Literal
42	Operation	operator: 44 operands: 45
43	ExprTuple	55, 47, 48, 46, 50
44	Literal
45	ExprTuple	55, 47, 48, 49, 50
46	Operation	operator: 52 operands: 51
47	Literal
48	Literal
49	Operation	operator: 52 operands: 53
50	Literal
51	ExprTuple	55, 54
52	Literal
53	ExprTuple	55, 56
54	Operation	operator: 65 operand: 59
55	Literal
56	Operation	operator: 65 operand: 60
57	ExprTuple	59
58	ExprTuple	60
59	Operation	operator: 61 operands: 62
60	Variable
61	Literal
62	ExprTuple	63, 64
63	Operation	operator: 65 operand: 67
64	Literal
65	Literal
66	ExprTuple	67
67	Variable