\begin{filecontents*}{test.csv}
    First ,   4 , 0 ,  2 , 5
    Second ,  0 , 0 ,  7 , 8
    Third ,   5 , 0 ,  6 ,
    Fourth , -5 , 0 , -6 ,
\end{filecontents*}


\documentclass{article}

\ExplSyntaxOn
% Step 1: reading the file
\tl_new:N \l__diaa_tmpa_tl
\ior_new:N \l__diaa_csv_ior
\bool_new:N \l__diaa_csv_str_bool
\bool_new:N \l__diaa_empty_item_bool
\seq_new:N \l__diaa_csv_tmp_seq

% str mode (bool/star), key column, label, value columns, file
\NewDocumentCommand \ReadCSV { s O{1} m O{} m }
{
    \IfBooleanTF {#1}
    { \bool_set_true:N \l__diaa_csv_str_bool }
    { \bool_set_false:N \l__diaa_csv_str_bool }
    \diaa_csv_read:nnnn {#3} {#2} {#4} {#5}
}

% label, key column, value columns, file
\cs_new_protected:Npn \diaa_csv_read:nnnn #1 #2 #3 #4
{
    \tl_if_blank:nTF {#3}       % Detect number of columns and use 2 to last
    {
        \ior_open:NnTF \l__diaa_csv_ior {#4}
        {
            \bool_if:NTF \l__diaa_csv_str_bool
            { \ior_str_get:NN }
            { \ior_get:NN }
            \l__diaa_csv_ior \l__diaa_tmpa_tl

            \ior_close:N \l__diaa_csv_ior
            \seq_set_split:NnV \l_tmpa_seq { , } \l__diaa_tmpa_tl
            \seq_clear:N \l__diaa_csv_tmp_seq
            \int_step_inline:nnn { 2 } { \seq_count:N \l_tmpa_seq }
            { \seq_put_right:Nn \l__diaa_csv_tmp_seq {##1} }
        }
        { \msg_expandable_error:nnn { diaa } { file-not-found } {#4} }
    }
    { \seq_set_split:Nnn \l__diaa_csv_tmp_seq { , } {#3} } % explicit columns

    \ior_open:NnTF \l__diaa_csv_ior {#4}
    {
        \prop_new:c { g__diaa_csv_#1_prop }
        \__diaa_csv_read:nn {#1} {#2}
        \ior_close:N \l__diaa_csv_ior
    }
    { \msg_expandable_error:nnn { diaa } { file-not-found } {#4} }
}

\msg_new:nnn { diaa } { file-not-found }
{ File~`#1'~not~found. }

\cs_generate_variant:Nn \prop_put:Nnn { cxV }

% label, key column
\cs_new_protected:Npn \__diaa_csv_read:nn #1 #2
{
    \bool_if:NTF \l__diaa_csv_str_bool
    { \ior_str_map_inline:Nn }
    { \ior_map_inline:Nn }
    \l__diaa_csv_ior
    {
        \seq_set_split:Nnn \l_tmpa_seq { , } {##1} % split one CSV row
        \tl_clear:N \l__diaa_tmpa_tl
        \seq_map_inline:Nn \l__diaa_csv_tmp_seq
        {
            \tl_put_right:Nx \l__diaa_tmpa_tl { { \seq_item:Nn \l_tmpa_seq {####1} } }
        }
        \prop_put:cxV { g__diaa_csv_#1_prop }
        { \seq_item:Nn \l_tmpa_seq {#2} }
        \l__diaa_tmpa_tl
    }
}

%%%%%%%%%%%%%%%%%%%%%%%%

% https://tex.stackexchange.com/a/634894/2288

\keys_define:nn { diaa / getPolyFromRow }
{
    global-assignment .bool_set:N = \l__diaa_gpfr_global_assignment_bool,
    global-assignment .default:n = true,
    global-assignment .initial:n = false,
    variable .tl_set:N = \l__diaa_gpfr_variable_name_tl,
    variable .value_required:n = true,
    variable .initial:n = X,
    typographical-variant .str_set:N = \l__diaa_gpfr_typographical_variant_str,
    typographical-variant .value_required:n = true,
    typographical-variant .initial:n = default,
}

% \getPolyFromRow will temporarily store the result in this variable. This
% allows us not to lose the result when the group started for \keys_set:nn
% ends (if the user chose to perform a local assignment, this must be done
% after closing that group).
\tl_new:N \g__diaa_gpfr_result_tl


% Options, macro for result, key, datafile label
\NewDocumentCommand \getPolyFromRow { O{} m m m }
{
    \group_begin:
    \keys_set:nn { diaa / getPolyFromRow } {#1}

    % Globally define _gfunc function aliases that perform global or local
    % assignments depending on \l__diaa_gpfr_global_assignment_bool. They
    % will be used *after* we close the current group.
    \bool_set_true:N \l__diaa_gpfr_dtfa_global_aliases_bool
    \__diaa_gpfr_define_tl_func_aliases:

    % Store the result in \g__diaa_gpfr_result_tl for now.
    \bool_set_true:N \l__diaa_gpfr_global_assignment_bool
    \diaa_get_poly_from_row:Nnn \g__diaa_gpfr_result_tl {#3} {#4}
    \group_end:

    % Use the globally-defined aliases to perform the user-chosen (local or
    % global) kind of assignment.
    \__diaa_clear_gfunc:N #2    % make sure the tl var #2 is defined
    \__diaa_set_eq_gfunc:NN #2 \g__diaa_gpfr_result_tl % set it
}

% True to globally define the aliases and give them _gfunc names rather than
% _func
\bool_new:N \l__diaa_gpfr_dtfa_global_aliases_bool

\cs_new_protected:Npn \__diaa_gpfr_define_tl_func_aliases:
{
    \bool_if:NTF \l__diaa_gpfr_global_assignment_bool
    {
        \__diaa_gpfr_define_alias:nnN { clear }     { N }  \tl_gclear_new:N
        \__diaa_gpfr_define_alias:nnN { set_eq }    { NN } \tl_gset_eq:NN
        \__diaa_gpfr_define_alias:nnN { put_right } { Nn } \tl_gput_right:Nn
    }
    {
        \__diaa_gpfr_define_alias:nnN { clear }     { N }  \tl_clear_new:N
        \__diaa_gpfr_define_alias:nnN { set_eq }    { NN } \tl_set_eq:NN
        \__diaa_gpfr_define_alias:nnN { put_right } { Nn } \tl_put_right:Nn
    }
}

% Locally or globally define an alias for a function. The alias is defined
% globally with a gfunc name if \l__diaa_gpfr_dtfa_global_aliases_bool is true.
%
% #1: stem such as “clear”, “put_right”, etc.
% #2: signature of the alias (e.g., “Nn”)
\cs_new_protected:Npn \__diaa_gpfr_define_alias:nnN #1#2
{
    \bool_if:NTF \l__diaa_gpfr_dtfa_global_aliases_bool
    { \cs_gset_eq:cN }
    { \cs_set_eq:cN }
    {
        __diaa_#1_
        \bool_if:NT \l__diaa_gpfr_dtfa_global_aliases_bool { g }
        func:#2
    }
}

\int_new:N \l__diaa_gpfr_degree_int
\cs_generate_variant:Nn \__diaa_put_right_func:Nn { Nx }
\cs_generate_variant:Nn \__diaa_get_poly_from_row_append_monomial:Nnn { NnV }

% Macro for result, key, datafile label
\cs_new_protected:Npn \diaa_get_poly_from_row:Nnn #1#2#3
{
    % Locally define function aliases that perform global or local assignments
    % depending on \l__diaa_gpfr_global_assignment_bool: \__diaa_clear_func:Nn,
    % \__diaa_put_right_func:Nn, etc.
    \bool_set_false:N \l__diaa_gpfr_dtfa_global_aliases_bool
    \__diaa_gpfr_define_tl_func_aliases:

    \prop_get:cnN { g__diaa_csv_#3_prop } {#2} \l__diaa_tmpa_tl % the coefficients

    % Let's put (1 + degree) for now in this int variable.
    \int_zero:N \l__diaa_gpfr_degree_int
    \tl_map_inline:Nn \l__diaa_tmpa_tl
    {
        \tl_if_empty:nT {##1} { \tl_map_break: }
        \int_incr:N \l__diaa_gpfr_degree_int
    }

    \__diaa_clear_func:N #1        % initialize #1 as a tl var if necessary
    \bool_set_false:N \l_tmpa_bool % true: add + operator if next coeff is > 0

    \tl_map_inline:Nn \l__diaa_tmpa_tl % loop over the coefficients
    {
        % Degree of the monomial we're about to output
        \int_decr:N \l__diaa_gpfr_degree_int
        % Early termination condition if the row is not full of coefficients
        \int_compare:nNnT { \l__diaa_gpfr_degree_int } < { 0 }
        { \tl_map_break: }

        \fp_compare:nNnF {##1} = { 0 }
        {
            % Insert a + operator if necessary
            \bool_if:NTF \l_tmpa_bool
            {
                \fp_compare:nNnT {##1} > { 0 }
                { \__diaa_put_right_func:Nn #1 { + } }
            }
            { \bool_set_true:N \l_tmpa_bool }

            % Insert the monomial
            \__diaa_get_poly_from_row_append_monomial:NnV #1 {##1}
            \l__diaa_gpfr_variable_name_tl
        }
    }
}

\msg_new:nnn { diaa } { gpfr-unknown-typo-variant }
{ Unknown~typographical~variant~for~\token_to_str:N \getPolyFromRow :~`#1'. }

\cs_generate_variant:Nn \str_case_e:nnF { V }
\cs_generate_variant:Nn \msg_error:nnn { nnV }

% Macro, coefficient, variable name
\cs_new_protected:Npn \__diaa_get_poly_from_row_append_monomial:Nnn #1#2#3
{
    \str_case_e:VnF \l__diaa_gpfr_typographical_variant_str
    {
        { default }     { \tl_set:Nn \l__diaa_tmpa_tl { #2 \times #3 ^ } }
        { with-braces } { \tl_set:Nn \l__diaa_tmpa_tl { #2 \times {#3} ^ } }
    }
    {
        \msg_error:nnV { diaa } { gpfr-unknown-typo-variant }
        \l__diaa_gpfr_typographical_variant_str
    }

    \__diaa_put_right_func:Nx #1
    {
        \int_case:nnF { \l__diaa_gpfr_degree_int } % depending on the degree...
        {
            { 0 } { \exp_not:n {#2} } % degree 0 → only the coefficient
            { 1 } { \exp_not:n { #2 \times #3 } }
        }
        { % Other degrees
            \exp_not:V \l__diaa_tmpa_tl % use the selected variant
            % Use braces in case the exponent has several digits
            { \int_use:N \l__diaa_gpfr_degree_int }
        }
    }
}

%%%%%%%%%%%%%%%%%%%%%

% Step 2: getting the values
% star → global assignment, macro or tl var, value column, key, label
\NewDocumentCommand \getValue { s m O{1} m m }
{
    \IfBooleanTF {#1} { \tl_gset:Nx } { \tl_set:Nx }
    #2 { \diaa_csv_item:nnn {#4} {#3} {#5} }
    \tl_if_empty:NT #2
    { \msg_warning:nnnnn { diaa } { item-empty } {#3} {#4} {#5} }
}

% key, value column, label
\NewExpandableDocumentCommand \CSVItem { m O{1} m }
{ \diaa_csv_item:nnn {#1} {#2} {#3} }

% Version with error if empty
% \NewExpandableDocumentCommand \CSVItem { m O{1} m }
%   {
    %     \exp_args:Nf \__diaa_check_empty_item:nnnn
    %       { \diaa_csv_item:nnn {#1} {#2} {#3} } {#2} {#1} {#3}
    %   }
% \cs_new:Npn \__diaa_check_empty_item:nnnn #1 #2 #3 #4
%   {
    %     \tl_if_empty:nTF {#1}
    %       { \msg_expandable_error:nnnnn { diaa } { item-empty } {#2} {#3} {#4} }
    %       {#1}
    %   }

\cs_generate_variant:Nn \tl_item:nn { f }

% key, value column, label
\cs_new:Npn \diaa_csv_item:nnn #1 #2 #3
{
    \prop_if_exist:cTF { g__diaa_csv_#3_prop }
    {
        \prop_if_in:cnTF { g__diaa_csv_#3_prop } {#1}
        {
            \exp_args:NNf \__diaa_check_column_range:Nnn \use_i:nn
            { \prop_item:cn { g__diaa_csv_#3_prop } {#1} } {#2}
        }
        { \msg_expandable_error:nnnn { diaa } { key-undefined } {#1} {#3} }
    }
    { \msg_expandable_error:nnn { diaa } { csv-undefined } {#3} }
}

\cs_new:Npn \__diaa_check_column_range:Nnn #1 #2 #3
{
    \bool_lazy_or:nnTF
    { \int_compare_p:nNn {#3} = { 0 } }
    { \int_compare_p:nNn { \tl_count:n {#2} } < { \int_abs:n {#3} } }
    { \msg_expandable_error:nnn { diaa } { out-of-range } {#3} }
    { \exp_args:Nf #1 { \tl_item:nn {#2} {#3} } {#3} }
}

\msg_new:nnn { diaa } { csv-undefined } { CSV~database~''#1''~is~undefined! }
\msg_new:nnn { diaa } { key-undefined } {Parameter~''#1''~is~not~found~in~CSV~''#2''! }
\msg_new:nnn { diaa } { out-of-range } { Column~#1~is~out~of~range! }
%\msg_new:nnn { diaa } { item-empty }
%{ Column~#1~of~''#2''~in~CSV~''#3''~is~empty! }
\msg_new:nnn { diaa } { item-empty }
{ Empty~column~#1~of~''#2''~in~CSV~''#3''! }%Item~#1~from~`#2'~in~CSV~`#3'~is~empty!
\msg_new:nnn { diaa } { empty-row-item }
{ Empty~item~#1~\msg_line_context:! }
\msg_new:nnn { diaa } { row-empty }
{ Empty~parameter~''#1''~in~CSV~''#2''! }


\cs_new:Npn \__diaa_check_empty:nn #1 #2
{
    \tl_if_empty:nT {#1}
    { \msg_warning:nnn { diaa } { empty-row-item } {#2} }
    #1
}

% star → global assignment, macro, key, label
\NewDocumentCommand \getRow { s m m m }
{
    \prop_if_exist:cTF { g__diaa_csv_#4_prop }
    {
        \prop_get:cnNTF { g__diaa_csv_#4_prop } {#3} \l__diaa_tmpa_tl
        {
            \bool_set_true:N \l__diaa_empty_item_bool
            \tl_map_inline:Nn \l__diaa_tmpa_tl
            {
                \tl_if_empty:nF {##1}
                { \bool_set_false:N \l__diaa_empty_item_bool }
            }
            \bool_if:NT \l__diaa_empty_item_bool
            { \msg_warning:nnnn { diaa } { row-empty } {#3} {#4} }
            \IfBooleanTF {#1} { \cs_gset_nopar:Npx } { \cs_set_nopar:Npx } #2 [ ##1 ]
            {
                \exp_not:N \str_if_eq:nnTF {##1} { non-empty }
                {
                    \exp_not:N \__diaa_nb_nonempty_items_in_row:nw { 0 }
                    \exp_not:V \l__diaa_tmpa_tl
                    \exp_not:n { \q_recursion_tail \q_recursion_stop }
                }
                {
                    \exp_not:N \__diaa_check_column_range:Nnn
                    \exp_not:N \__diaa_check_empty:nn
                    { \exp_not:V \l__diaa_tmpa_tl } {##1}
                }
            }
        }
        { \msg_expandable_error:nnnn { diaa } { key-undefined } {#3} {#4} }
    }
    { \msg_expandable_error:nnn { diaa } { csv-undefined } {#4} }
}


\cs_new:Npn \__diaa_nb_nonempty_items_in_row:nw #1#2
{
    \quark_if_recursion_tail_stop_do:nn {#2} { \int_eval:n {#1} }
    \tl_if_empty:nTF {#2}
    { \__diaa_nb_nonempty_items_in_row:nw {#1} }
    { \__diaa_nb_nonempty_items_in_row:nw { #1 + 1 } }
}
\ExplSyntaxOff


\begin{document}
    \getPolyFromRow{\firstPoly}{First}{mydata}%
    The first polynom is $\firstPoly$.

    \getPolyFromRow[variable=v]{\secondPoly}{Second}{mydata}%
    The second polynom is $\secondPoly$.

    \getValue\First{First}{mydata}
    \First

    \getRow{\RowThird}{Third}{mydata}
    \RowThird
\end{document}