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
from proveit.numbers import Add, Exp, Mult, e, i, one, pi, two
from proveit.physics.quantum import NumKet, ket1
from proveit.physics.quantum.QPE import _phase, two_pow_t

# build up the expression from sub-expressions
sub_expr1 = Add(k, two_pow_t)
expr = ExprTuple(ScalarMult(Exp(e, Mult(two, pi, i, _phase, sub_expr1)), NumKet(sub_expr1, Add(t, one))), ScalarMult(Mult(Exp(e, Mult(two, pi, i, _phase, k)), Exp(e, Mult(two, pi, i, _phase, two_pow_t))), TensorProd(ket1, NumKet(k, t))))

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(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot \left(k + 2^{t}\right)} \cdot \lvert k + 2^{t} \rangle_{t + 1}, \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot 2^{t}}\right) \cdot \left(\lvert 1 \rangle {\otimes} \lvert k \rangle_{t}\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: 4 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	8, 9
6	Operation	operator: 44 operands: 10
7	Operation	operator: 27 operands: 11
8	Operation	operator: 37 operands: 12
9	Operation	operator: 13 operands: 14
10	ExprTuple	31, 15
11	ExprTuple	29, 16
12	ExprTuple	17, 18
13	Literal
14	ExprTuple	19, 20
15	Operation	operator: 37 operands: 21
16	Operation	operator: 34 operands: 22
17	Operation	operator: 44 operands: 23
18	Operation	operator: 44 operands: 24
19	Operation	operator: 25 operand: 33
20	Operation	operator: 27 operands: 28
21	ExprTuple	46, 40, 41, 42, 29
22	ExprTuple	47, 33
23	ExprTuple	31, 30
24	ExprTuple	31, 32
25	Literal
26	ExprTuple	33
27	Literal
28	ExprTuple	39, 47
29	Operation	operator: 34 operands: 35
30	Operation	operator: 37 operands: 36
31	Literal
32	Operation	operator: 37 operands: 38
33	Literal
34	Literal
35	ExprTuple	39, 43
36	ExprTuple	46, 40, 41, 42, 39
37	Literal
38	ExprTuple	46, 40, 41, 42, 43
39	Variable
40	Literal
41	Literal
42	Literal
43	Operation	operator: 44 operands: 45
44	Literal
45	ExprTuple	46, 47
46	Literal
47	Variable