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, k, t
from proveit.linear_algebra import ScalarMult, TensorProd, VecAdd, VecSum
from proveit.numbers import Exp, Interval, Mult, e, frac, i, one, pi, subtract, two, zero
from proveit.physics.quantum import NumKet, ket0, ket1
from proveit.physics.quantum.QPE import _phase, two_pow_t

# build up the expression from sub-expressions
expr = ExprTuple(frac(one, Exp(two, frac(t, two))), TensorProd(VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, _phase, two_pow_t)), ket1)), VecSum(index_or_indices = [k], summand = ScalarMult(Exp(e, Mult(two, pi, i, _phase, k)), NumKet(k, t)), domain = Interval(zero, subtract(two_pow_t, one)))))

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