logo

Expression of type InSet

from the theory of proveit.physics.quantum.QPE

In [1]:
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 m
from proveit.linear_algebra import LinMap
from proveit.logic import CartExp, InSet
from proveit.numbers import Complex
from proveit.physics.quantum import NumBra, Qmult
from proveit.physics.quantum.QFT import InverseFourierTransform
from proveit.physics.quantum.QPE import _t, _two_pow_t
In [2]:
# build up the expression from sub-expressions
expr = InSet(Qmult(Qmult(NumBra(m, _t), InverseFourierTransform(_t))), LinMap(CartExp(Complex, _two_pow_t), Complex))
expr:
In [3]:
# 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
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\left[{_{t}}\langle m \rvert \thinspace {\mathrm {FT}}^{\dag}_{t}\right] \in \mathcal{L}\left(\mathbb{C}^{2^{t}}, \mathbb{C}\right)
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(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')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
directionDirection of the relation (normal or reversed)normalnormal('with_direction_reversed', 'is_reversed')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4
3Operationoperator: 10
operand: 8
4Operationoperator: 6
operands: 7
5ExprTuple8
6Literal
7ExprTuple9, 16
8Operationoperator: 10
operands: 11
9Operationoperator: 12
operands: 13
10Literal
11ExprTuple14, 15
12Literal
13ExprTuple16, 17
14Operationoperator: 18
operands: 19
15Operationoperator: 20
operand: 26
16Literal
17Operationoperator: 22
operands: 23
18Literal
19ExprTuple24, 26
20Literal
21ExprTuple26
22Literal
23ExprTuple25, 26
24Variable
25Literal
26Literal